The objectives of this study, which is an outgrowth of the North American Carotid Endarteractomy Trial, are to determine if, among patients who undergo carotid endarterectomy, the risk of stroke and death in the 30 day perioperative period and in the first 3 months after surgery, is influenced by the prescription of high doses of aspirin vs. low doses started prior to surgery and continued for three months. This is a blinded, randomized, controlled, multicenter trial; prior to surgery, patients will be randomized to one of four treatment groups which will differ only in the dose of aspirin prescribed.